Washington (CNN) -- Vice President Joe Biden huddled behind closed doors with top congressional budget negotiators Thursday, seeking to bridge a cavernous partisan divide over taxes and spending before the federal government slams into its debt ceiling this summer.

Maryland Rep. Chris Van Hollen and South Carolina Rep. James Clyburn -- both part of the House Democratic leadership -- also took part in the meeting.

President Barack Obama has said he hopes the talks will lead to an agreement by June.

"We have to make some real progress," Biden said at the start of the meeting, held across the street from the White House. It's time "to try and deal with the hard business of what's at hand here."

"Let's make sure each of us understands where the other guy is coming from," he said.

Cantor told reporters he thinks "there is a fairly clear sense of where we need to head, and that is to find some common ground."

"We are trying to find ways to produce a result," he insisted.

Leaders of both parties are struggling to come up with a common deficit reduction strategy that won't alienate their political bases. Democrats have excoriated House Republicans for passing a fiscal year 2012 budget that the Democrats claim would undermine Medicare and shred seniors' economic safety net. Republicans, in turn, have blasted Obama's fiscal blueprint, claiming it lacks serious deficit reduction measures.

Democrats and Republicans agreed last month to a package of $38.5 billion in spending cuts covering the remainder of the current fiscal year. GOP lawmakers, however, are balking at the idea of raising the country's current $14.294 trillion debt ceiling without a commitment to further reductions.

"We will not increase the debt limit without real spending cuts and budget reforms," said House Speaker John Boehner, R-Ohio. "I think Americans simply will not stand for it, and they shouldn't."

The administration, in contrast, has called for a "clean" vote on the cap, which would raise the limit without adding any conditions. Democrats have warned their GOP counterparts not to play a game of "chicken" with the economy. Geithner has warned of "catastrophic" consequences if the limit is not raised, including skyrocketing interest rates.

Geithner has said the government is on track to hit the current ceiling by May 16, though he recently indicated in a letter to Congress he can keep the country out of default until August 2.

Fiscal year 2011 ends September 30.

The current GOP proposal for fiscal year 2012, drafted by House Budget Committee Chairman Paul Ryan, R-Wisconsin, would overhaul key portions of the tax code, dropping the top rate for individuals and businesses to 25% while eliminating a number of loopholes.

Domestic discretionary spending -- the share of the budget not devoted to entitlements -- would remain frozen below 2008 levels. Overall spending would be reduced by approximately $6 trillion over the next 10 years.

The most contentious parts of Ryan's blueprint, however, revolve around its proposed changes to Medicare and Medicaid. Medicare, a major contributor to spiraling federal deficits, would be overhauled starting in 2022. The government would no longer directly pay bills for senior citizens in the program. Instead, recipients would choose a plan from a list of private providers, which the federal government would subsidize.

Individuals currently 55 or older would not be affected by the changes.

Medicaid, which provides health care for the disabled and the poor, would be transformed into a series of block grants to the states. Republicans believe that state governments would spend the money more efficiently and would benefit from increased flexibility, while Democrats warn that the move would shred the health care security provided to the most vulnerable Americans in recent generations.

Obama's plan, in sharp contrast to Ryan's, would repeal the Bush-era tax cuts on families making more than $250,000 annually, something sought by Democrats but strongly opposed by Republicans.

The president has also called for the creation of a "debt fail-safe" trigger that would impose automatic across-the-board spending cuts and tax changes in coming years if annual deficits are on track to exceed 2.8% of the nation's gross domestic product.

Administration officials claim that by building on or adjusting the health care reform bill passed last year, $480 billion would be saved by 2023, followed by an additional $1 trillion in the following decade. Obama has proposed tightly constraining the growth in Medicare costs starting in 2018.

Boehner said Thursday that "when it comes to increasing the debt limit and the need to have reductions in spending, nothing is off the table except raising taxes."

A spokesman for Cantor, Brad Dayspring, said the Ryan plan was put on the table as the "starting point in the negotiations."

However, a Republican aide highlighted one part of the Ryan plan, $715 billion worth of cuts in mandatory domestic spending, as a possible area of common ground with Democrats and the White House. That total excludes the controversial Medicare and Medicaid reforms, as well as GOP plans to repeal the president's health care overhaul.

It includes the elimination of a range of programs, however, including $46.5 billion in college student subsidies, $29.6 billion for housing giants Fannie Mae and Freddie Mac, and $4.5 billion for the new Consumer Financial Protection Bureau, according to the Republican aide.

Cantor denied reports that the Republicans have already backed away from their Medicare plan. Democrats, who control both the Senate and the White House, have repeatedly said the idea has no chance of being enacted.